Dưới đây là khai triển và rút gọn các biểu thức trong bài toán:

1. \((x^2 - 1)(x^4 + x^2 + 1)\)
\[
= x^6 + x^4 + x^2 - x^4 - x^2 - 1
= x^6 - 1
\]

2. \((2xy + 2)(4x^2y^2 - 4xy + 4)\)
\[
= 2(2xy + 1)(4x^2y^2 - 4xy + 4)
= 2(8x^3y^3 - 8x^2y^2 + 8xy + 4x^2y^2 - 4xy + 4)
= 16x^3y^3 - 8x^2y^2 + 8xy + 4x^2y^2 - 4xy + 4
= 16x^3y^3 - 4x^2y^2 + 4xy + 4
\]

3. \((x - 5)(x + 5) - (x - 4)(x^2 + 4x + 16)\)
\[
= (x^2 - 25) - (x^3 + 4x^2 + 16x - 4x^2 - 16x - 64)
= x^2 - 25 - x^3 + 64
= -x^3 + x^2 + 39
\]

4. \((a + b)(a^2 - ab + b^2) - a(a - b)(a + b)\)
\[
= a^3 + b^3 - a(a^2 - b^2)
= a^3 + b^3 - a^3 + ab^2
= b^3 + ab^2
\]

5. \((2x + 3)^2(6 - 4)(x + 4) + (-1)(x^2 + x + 1)\)
\[
= 4(2x + 3)^2(x + 4) - (x^2 + x + 1)
= 4(4x^2 + 12x + 9)(x + 4) - (x^2 + x + 1)
= 4(4x^3 + 16x^2 + 48x + 36) - (x^2 + x + 1)
= 16x^3 + 64x^2 + 192x + 144 - x^2 - x - 1
= 16x^3 + 63x^2 + 191x + 143
\]

6. \((x - 2)(x^2 + 2x + 4) + (x - 3)(x + 3)\)
\[
= (x^3 + 2x^2 + 4x - 2x^2 - 4x - 8) + (x^2 - 9)
= x^3 - 8 + x^2 - 9
= x^3 + x^2 - 17
\]

7. \((2x + 3)(2x - 3) + (4x - 1)(16x^2 + 4x + 1)\)
\[
= (4x^2 - 9) + (64x^3 + 16x^2 + 4x - 16x^2 - 4x - 1)
= 4x^2 - 9 + 64x^3 - 1
= 64x^3 + 4x^2 - 10
\]